Question relating to direction of magnetic force on moving charge

Hi
I have always been very curious if anybody knows why the magnetic force on a moving charged particle in a magnetic field is always perpendicular to the plane containing the magnetic field's vector and the charged particles velocity vector.
Any help would be greatly appreciated.
Thanks
Parsa

Staff: Mentor

A force component parallel to the velocity in a pure magnetic field (in our lab frame) would increase (or decrease) the energy of the particle, without any potential difference for this particle -> energy is not conserved.
A force component along the magnetic field would lead to a non-conservative force, as magnetic field lines are closed -> energy is not conserved.

A force component parallel to the velocity in a pure magnetic field (in our lab frame) would increase (or decrease) the energy of the particle, without any potential difference for this particle -> energy is not conserved.
A force component along the magnetic field would lead to a non-conservative force, as magnetic field lines are closed -> energy is not conserved.

Staff: Mentor

A force along the magnetic field lines leads to a potential drop along the field lines. You could follow that potential drop along the circular line, and arrive at the original point again - but with a lower potential. A potential cannot have two different values at the same point at the same time, so this is impossible.

Strictly speaking, we would have to include the velocity in the consideration, but that does not change the main issue.

I see how that makes it nonconservative. Thank you. You at least have given me a reason for why the force direction being perpendicular to the v-B plane would have made the most sense (or at least special) because it would have violated energy conservation if it wasn't in that direction.
Thank you